6 papers
Inexact Warped Resolvent iterations
Raul T. Marcavillaca, Fernando Roldan
In this paper we aim to solve structured monotone inclusions using inexact warped resolvents evaluated under a relative-error criterion. The resulting algorithms admit a geometric…
A strongly convergent inertial inexact proximal-point algorithm for monotone inclusions with applications to variational inequalities
M. Marques Alves, J. E. Navarro Caballero, M. Geremia +1
We propose an inertial variant of the strongly convergent inexact proximal-point (PP) method of Solodov and Svaiter (2000) for monotone inclusions. We prove strong convergence of o…
An inexact inertial projective splitting algorithm with strong convergence
M. Marques Alves, J. E. Navarro Caballero, R. T. Marcavillaca
We propose and study a strongly convergent inexact inertial projective splitting (PS) algorithm for finding zeros of composite monotone inclusion problems involving the sum of fini…
Heavy Ball and Nesterov Accelerations with Hessian-driven Damping for Nonconvex Optimization
N. Hadjisavvas, F. Lara, R. T. Marcavillaca +1
In this work, we investigate a second-order dynamical system with Hessian-driven damping tailored for a class of nonconvex functions called strongly quasiconvex. Buil\-ding upon th…
Strongly quasiconvex functions: what we know (so far)
Sorin-Mihai Grad, Felipe Lara, Raúl T. Marcavillaca
Introduced by Polyak in 1966, the class of strongly quasiconvex functions includes some interesting nonconvex members, like the square root of the Euclidean norm or ratios with a n…
Characterizations, Dynamical Systems and Gradient Methods for Strongly Quasiconvex Functions
Felipe Lara, Raúl T. Marcavillaca, Phan T. Vuong
We study differentiable strongly quasiconvex functions for providing new properties for algorithmic and monotonicity purposes. Furthemore, we provide insights into the decreasing b…